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    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "\n# 1D Unbalanced optimal transport\n\nThis example illustrates the computation of Unbalanced Optimal transport\nusing a Kullback-Leibler relaxation.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "# Author: Hicham Janati <hicham.janati@inria.fr>\n#\n# License: MIT License\n\n# sphinx_gallery_thumbnail_number = 4\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\nimport ot.plot\nfrom ot.datasets import make_1D_gauss as gauss"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Generate data\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "n = 100  # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na = gauss(n, m=20, s=5)  # m= mean, s= std\nb = gauss(n, m=60, s=10)\n\n# make distributions unbalanced\nb *= 5.0\n\n# loss matrix\nM = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\nM /= M.max()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Plot distributions and loss matrix\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "pl.figure(1, figsize=(6.4, 3))\npl.plot(x, a, \"b\", label=\"Source distribution\")\npl.plot(x, b, \"r\", label=\"Target distribution\")\npl.legend()\n\n# plot distributions and loss matrix\n\npl.figure(2, figsize=(5, 5))\not.plot.plot1D_mat(a, b, M, \"Cost matrix M\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Solve Unbalanced Sinkhorn\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "# Sinkhorn\n\nepsilon = 0.1  # entropy parameter\nalpha = 1.0  # Unbalanced KL relaxation parameter\nGs = ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha, verbose=True)\n\npl.figure(3, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Gs, \"UOT matrix Sinkhorn\")\n\npl.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## plot the transported mass\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "pl.figure(4, figsize=(6.4, 3))\npl.plot(x, a, \"b\", label=\"Source distribution\")\npl.plot(x, b, \"r\", label=\"Target distribution\")\npl.fill(x, Gs.sum(1), \"b\", alpha=0.5, label=\"Transported source\")\npl.fill(x, Gs.sum(0), \"r\", alpha=0.5, label=\"Transported target\")\npl.legend(loc=\"upper right\")\npl.title(\"Distributions and transported mass for UOT\")"
      ]
    }
  ],
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